Oblivious polynomial evaluation and oblivious neural learning

Abstract

We study the problem of Oblivious Polynomial Evaluation (OPE). There are two parties, Alice who has a polynomial P, and Bob who has an input x. The goal is for Bob to compute P(x) in such way that Alice learns nothing about x and Bob learns only what can be inferred from P(x). Previously existing protocols are based on some intractability assumptions that have not been well studied [15,14], and these protocols are only applicable for polynomials over finite fields. In this paper, we propose efficient OPE protocols which are based on Oblivious Transfer only. Unlike that of [15], slight modifications to our protocols immediately give protocols to handle multi-variate polynomials and polynomials over floating-point numbers. Many important real-world applications deal with floating-point numbers, instead of integers or arbitrary finite fields, and our protocols have the advantage of operating directly on floating-point numbers, instead of going through finite field simulation as that of [14]. As an example, we give a protocol for the problem of Oblivious Neural Learning, where one party has a neural network and the other, with some training set, wants to train the neural network in an oblivious way.